Official Historical SAT to IQ Conversions

These data were combined from two hard-to-obtain sources. The first was A
Study of Error: a Summary and Evaluation of Methods Used in Six Years of
Study of the Scholastic Aptitude Test of the College Entrance Examination
Board by Carl C. Brigham, Associate Secretary of the College Entrance
Examination Board (1932). The second was the Otis Self-Administering
Tests of Mental Ability (Higher
Examination, Form A) IQ Scales (1922-1928). Only raw scores were provided in the first source so the second source was needed to get the corresponding IQ scores. The following two paragraphs are a direct quote from the Study of Error, p.336:

It would be expected that a test designed for use in high schools
would not differentiate the upper range of college applicants and this
proved to be the case, although this is not a reflection upon the Otis
test. 1080 candidates were given the Otis test with a half-hour time limit.
The mean scholastic aptitude score of these candidates (randomly sampled)
was 499.213 and the sigma was 99.272. The mean Otis score was 58.7435,
sigma 8.6839. The correlation between the two examinations was .7931. As
the maximum possible score on the Otis examination was 75, the distribution
of Otis scores was cut off sharply at the upper end and high score candidates
probably were not completely differentiated.

Table XVIII gives the most probable scholastic aptitude
test score, percentile, and letter grade for each Otis total score. The Otis
I.Q. conversions were not used, and this table applies only to total raw
scores. The coefficient of correlation between the Otis test and the Board
test (.7931) means considerable uncertainty in predicting one score from
another. The probable error of estimating a scholastic aptitude test score
from an Otis score is about 40. A "Predicted" S.A.T. score from an Otis score
of 50, for example, would be 420±40. This means that the chances are even that
the true S.A.T. score is between 380 and 460. The chances are also even that
the score is greater than 460 or less than 380, but become increasingly
smaller as the distance from these numbers becomes larger.

Otis Raw Score

Otis IQ

SAT score

SAT %ile

Otis Raw Score

Otis IQ

SAT score

SAT %ile

Otis Raw Score

Otis IQ

SAT score

SAT %ile

75

144

647

92

58

116

492

46

41

99

338

5

74

140

638

91

57

115

483

43

40

98

329

4

73

137

628

90

56

114

474

39

39

97

320

3

72

135

619

88

55

113

465

36

38

96

311

2

71

133

610

86

54

112

456

32

37

95

302

2

70

131

601

84

53

111

447

29

36

94

293

1

69

129

592

82

52

110

438

26

35

93

284

1

68

127

583

79

51

109

429

24

34

92

275

1

67

125

574

77

50

108

420

21

33

91

266

0.9

66

124

565

74

49

107

411

18

32

90

257

0.7

65

123

556

71

48

106

402

16

31

89

248

0.5

64

122

547

68

47

105

393

14

30

88

239

0.4

63

121

538

64

46

104

384

12

29

87

230

0.3

62

120

529

61

45

103

375

10

28

86

220

0.2

61

119

520

58

44

102

366

8

27

85

211

0.1

60

118

511

54

43

101

356

7

26

84

202

0.1

59

117

502

50

42

100

347

3

25

83

193

0.1

This table is of mainly historical interest because SAT scores have changed quite a bit since 1932. One lesson that can be drawn is about the uncertainty in converting scores between tests: the results are not very precise. Please keep this in mind when you are looking at my GRE and SAT (unofficial) estimation pages.